4x+8x^2=84

Solution for 4x+8x^2=84 equation:

4x+8x^2=84

We move all terms to the left:

4x+8x^2-(84)=0

a = 8; b = 4; c = -84;
Δ = b2-4ac
Δ = 42-4·8·(-84)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-52}{2*8}=\frac{-56}{16}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+52}{2*8}=\frac{48}{16}
=3
$